Dairy farmers are threatening to disrupt milk supplies during the Olympics in protest at planned milk price cuts, which they say will push them out of business.

Lobbying group Farmers for Action has warned that if prices are not restored to pre-April levels by 1 August they will disrupt the delivery of milk. David Handley, a welsh dairy farmer who is chairman of the organisation, told the BBC Radio 4 Farming Today programme: "If we don't get reinstatement, we are looking at disruption of milk supply. That could come in many forms and with us running into something that is very important to many people: the Olympics.

"Part of our action is likely to disrupt. That's unfortunate, but at the end of the day we are in desperation street."

His warning follows announcements in the past seven days from three dairy processing companies – Robert Wiseman Dairies, Arla Foods UK and Dairy Crest – that they intend to cut the prices paid to farmers for milk by 1.7p per litre, 2p per litre and 1.65p per litre respectively. The processors say the move, which follows cuts in April and June, is a result of deterioration in the commodity markets for skimmed milk powder and wholesale cream.

But groups representing farmers' interests to the processors say the cuts will mean milk prices are unsustainable, driving even more dairy farmers out of business. Their numbers have already dropped by 40% to 10,700 in the last 10 years. About three farmers a week left dairy farming in the year to May 2012, according to Food Standards Agency figures.

Jonathan Ovens, a dairy farmer and chairman of one such group – the Arla Foods Milk Partnership – said: "Farmers simply cannot afford to go into the winter making a loss of 5p per litre."

Dairy farmers enter contracts, typically lasting from three to 12 months, to supply milk to processors. While these contracts ensure they have a buyer for their milk, the agreements do not fix the price over the term of the contract and processors can change the amount they pay without notice. One processor – Dairy Crest – gave just four days' notice of its previous cut.

Some of the major retailers – Tesco, Sainsbury's, Waitrose and Marks & Spencer – have corporate responsibility strategies which include terms to protect farmers. Tesco and Sainsbury's pay a price per litre that covers the cost of production, with Sainsbury's currently paying 30.56p per litre. Waitrose pays a market leading price, aiming to top the prices paid by the other retailers.

But Rob Newbery, chief dairy adviser for the National Farmers Union, said that the three processors involved in these cuts supply milk to the Co-op, Morrisons and Asda, which do operate in the same way. "They claim to work with farmers, but at the moment because they pay the processors' own prices plus a small premium, it's dragged the price paid to farmers below the cost of production – to about 25p per litre," he said.

A Morrisons spokesperson said: "To ease the pressure on dairy farmers we pay a penny premium for every litre of milk we buy, which the processors distribute among their non-aligned producers groups. We have also extended our milk contracts to 2015, providing long-term security to farmers."

A spokesperson for the Co-operative said: "We are doing everything we can to attempt to alleviate the pressures facing dairy farmers during these tough trading conditions. Earlier this week we took the decision that we would, from 1 August, increase the premium we pay on milk to farmers by 0.65p per litre, taking it to 2p per litre – the farmers we deal with have now been notified of this.

"We remain in constant dialogue with farmers, and will keep the situation under review."

The average cow produces 7,500 litres of milk a year, meaning an annual loss of £375 per cow or £45,000 for a typical herd of 120 cows. Newbery says the cold wet spring and summer has already made life difficult for dairy farmers, who have been unable to make silage and have had to bring their cows in early because of wet under-foot conditions. At the same time they have suffered steep inflation in energy, feed and fertiliser costs.

"They can't face the winter with these losses," he said. "Scale is irrelevant. We don't see this as driving a move to large-scale business, but threatening the future of the UK dairy industry."

The NFU says it will support peaceful and lawful protest, and has joined the call for milk prices to be reinstated to pre-April levels. About 2,000 NFU members will converge on London next week to meet the department for the environment, food and rural affairs minister Jim Paice, and call for fair dealings between farmers and dairy companies.